Problem: What is the period of $y = \sin 5x $?
Explanation: The graph of $y = \sin 5x$ passes through one full period as $5x$ ranges from $0$ to $2\pi$, which means $x$ ranges from $0$ to $\boxed{\frac{2\pi}{5}}.$

The graph of $y = \sin 5x$ is shown below:

[asy]
import TrigMacros;

size(400);

real g(real x)
{
	return sin(5*x);
}

draw(graph(g,-3*pi,3*pi,n=700,join=operator ..),red);
trig_axes(-3*pi,3*pi+.4,-2,2,pi,1);
layer();
rm_trig_labels(-3, 3, 1);
[/asy]